A kettle containing 1 kg of water has just reached its boiling point. How much energy, in joules, is required to boil the kettle dry?
Q=L•m,
where L = 2257 kJ/kg is heat of vaporization
To calculate the energy required to boil the kettle dry, we need to consider the energy needed to raise the temperature of the water to its boiling point and then the energy needed to undergo the phase change from liquid to vapor.
Let's break it down step-by-step:
Step 1: Calculate the energy required to raise the temperature of the water to its boiling point:
The specific heat capacity of water is approximately 4,186 J/kg·°C.
The initial temperature of the water is assumed to be 25°C, and the boiling point of water is 100°C. Therefore, the temperature change is:
ΔT = 100°C - 25°C = 75°C
The energy required to raise the temperature of the water is given by the formula:
Q = mass × specific heat capacity × ΔT
where:
Q is the energy in joules,
mass is the mass of water in kilograms, and
ΔT is the temperature change in degrees Celsius.
We have:
mass = 1 kg
specific heat capacity = 4,186 J/kg·°C
ΔT = 75°C
Plugging in the values:
Q1 = 1 kg × 4,186 J/kg·°C × 75°C
Step 2: Calculate the energy required for the phase change:
The energy required for the phase change is given by the formula:
Q2 = mass × latent heat of vaporization
where:
Q2 is the energy in joules,
mass is the mass of water in kilograms,
and latent heat of vaporization for water is approximately 2,260,000 J/kg.
Plugging in the values:
Q2 = 1 kg × 2,260,000 J/kg
Step 3: Calculate the total energy required:
To calculate the total energy required, we sum up the energy required for raising the temperature and the energy required for the phase change:
Total energy = Q1 + Q2
Plugging in the calculated values:
Total energy = Q1 + Q2 = (1 kg × 4,186 J/kg·°C × 75°C) + (1 kg × 2,260,000 J/kg)
Calculating the values:
Total energy = 314,150 J + 2,260,000 J
Therefore, the total energy required to boil the kettle dry is approximately 2,574,150 joules.
To find the amount of energy required to boil the kettle dry, we need to consider the energy needed to raise the temperature of the water from room temperature (assuming approximately 25 degrees Celsius) to its boiling point and the energy required to change the state of the water from liquid to gas.
First, let's calculate the energy required to raise the temperature of the water to its boiling point using the specific heat capacity of water. The specific heat capacity of water is approximately 4.18 joules per gram per degree Celsius.
Given that the kettle contains 1 kg (1000 grams) of water and assuming the room temperature is 25 degrees Celsius, we need to calculate the energy required to raise the temperature from 25 degrees Celsius to 100 degrees Celsius:
Energy = mass × specific heat capacity × temperature change
Energy = 1000 g × 4.18 J/g°C × (100°C - 25°C)
Energy = 1000 g × 4.18 J/g°C × 75°C
Energy = 313,500 J
So it takes 313,500 joules of energy to raise the temperature of the water to its boiling point.
Next, we need to consider the energy required to change the state of the water from liquid to gas. This is known as the latent heat of vaporization, which for water is approximately 2,260 joules per gram.
Given that the kettle contains 1 kg (1000 grams) of water, the energy required to boil the water dry is:
Energy = mass × latent heat of vaporization
Energy = 1000 g × 2,260 J/g
Energy = 2,260,000 J
Therefore, the total energy required to boil the kettle dry is the sum of the energy required to raise the temperature and the energy required for vaporization:
Total Energy = Energy to raise temperature + Energy for vaporization
Total Energy = 313,500 J + 2,260,000 J
Total Energy = 2,573,500 J
Thus, approximately 2,573,500 joules of energy are required to boil the kettle dry.